Identifier
Values
[1,0] => [2,1] => [2] => [1,1,0,0,1,0] => 0
[1,0,1,0] => [3,1,2] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,0] => [2,3,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0] => [4,1,2,3] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0] => [2,4,1,3] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0] => [4,3,1,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,0] => [2,3,4,1] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [3,2] => [1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,9,1,2,3,8,4,6,7] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,4,1,2,9,3,5,6,7] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 0
[] => [1] => [1] => [1,0,1,0] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.
Map
cycle type
Description
The cycle type of a permutation as a partition.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.